ln(x)+ln(1+2u)=ln(a)

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Solution for ln(x)+ln(1+2u)=ln(a) equation:


Simplifying
ln(x) + ln(1 + 2u) = ln(a)

Multiply ln * x
lnx + ln(1 + 2u) = ln(a)
lnx + (1 * ln + 2u * ln) = ln(a)
lnx + (1ln + 2lnu) = ln(a)

Reorder the terms:
1ln + 2lnu + lnx = ln(a)

Multiply ln * a
1ln + 2lnu + lnx = aln

Solving
1ln + 2lnu + lnx = aln

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-1aln' to each side of the equation.
1ln + 2lnu + -1aln + lnx = aln + -1aln

Reorder the terms:
-1aln + 1ln + 2lnu + lnx = aln + -1aln

Combine like terms: aln + -1aln = 0
-1aln + 1ln + 2lnu + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1a + 1 + 2u + x) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-1a + 1 + 2u + x)' equal to zero and attempt to solve: Simplifying -1a + 1 + 2u + x = 0 Reorder the terms: 1 + -1a + 2u + x = 0 Solving 1 + -1a + 2u + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1a + 2u + -1 + x = 0 + -1 Reorder the terms: 1 + -1 + -1a + 2u + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a + 2u + x = 0 + -1 -1a + 2u + x = 0 + -1 Combine like terms: 0 + -1 = -1 -1a + 2u + x = -1 Add 'a' to each side of the equation. -1a + 2u + a + x = -1 + a Reorder the terms: -1a + a + 2u + x = -1 + a Combine like terms: -1a + a = 0 0 + 2u + x = -1 + a 2u + x = -1 + a Add '-2u' to each side of the equation. 2u + -2u + x = -1 + a + -2u Combine like terms: 2u + -2u = 0 0 + x = -1 + a + -2u x = -1 + a + -2u Add '-1x' to each side of the equation. x + -1x = -1 + a + -2u + -1x Combine like terms: x + -1x = 0 0 = -1 + a + -2u + -1x Simplifying 0 = -1 + a + -2u + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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